A162612 Triangle read by rows in which row n lists n terms, starting with n^2+n-1, with gaps = n^2-1 between successive terms.

1, 5, 8, 11, 19, 27, 19, 34, 49, 64, 29, 53, 77, 101, 125, 41, 76, 111, 146, 181, 216, 55, 103, 151, 199, 247, 295, 343, 71, 134, 197, 260, 323, 386, 449, 512, 89, 169, 249, 329, 409, 489, 569, 649, 729, 109, 208, 307, 406, 505, 604, 703, 802, 901, 1000, 131, 251

Offset: 1

Author

Omar E. Pol, Jul 09 2009

Keywords

• easy
• nonn
• tabl

Comments

Note that the last term of the n-th row is the n-th cube A000578(n).

Examples

			Triangle begins:
   1;
   5,   8;
  11,  19,  27;
  19,  34,  49,  64;
  29,  53,  77, 101, 125;
  41,  76, 111, 146, 181, 216;
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000578, A028387, A159797, A159798, A162610, A162611, A162613.

Programs

Mathematica

Table[NestList[#+n^2-1&,n^2+n-1,n-1],{n,20}]//Flatten (* Harvey P. Dale, Mar 02 2024 *)

PARI

T(n,k)=n+k*(n^2-1) \\ Franklin T. Adams-Watters, Aug 06 2009

Formula

Sum_{k=1..n} T(n,k)= n*(n^3 + n^2 + n - 1)/2 (row sums). - R. J. Mathar, Jul 20 2009

Extensions

More terms from Franklin T. Adams-Watters, Aug 06 2009